Soutiendra publiquement ses travaux de thèse intitulés
Contributions to numerical differentiation using
orthogonal polynomials and its application to fault
detection and parameter identification
Soutenance prévue le Vendredi 2 décembre 2022 à 11h30
Lieu : Universität des Saarlandes
Lehrstuhl für Systemtheorie und Regelungstechnik
Campus A5 1, 66123 Sarrebruck, Allemagne
Salle : 1.03
devant le jury composé de :
M. Mamadou MBOUP Professeur des universités Rapporteur
M. Cédric JOIN Professeur des universités Rapporteur
M. Silviu-Iulian NICULESCU Directeur de recherche Examinateur
Mme Kathrin FLASSKAMP Professeure Examinatrice M. Hugues MOUNIER Professeur des universités Directeur de thèse
M. Joachim RUDOLPH Professeur Co-directeur de thèse
Abstract: The reconstruction of unmeasured quantities in dynamical systems often boils down to the knowledge of derivatives of the measured system variables. The approximation of these derivatives in the presence of measurement disturbances is known to be challenging. However, numerical differentiation algorithms based on orthogonal polynomials and truncated generalised Fourier series may considerably simplify the problem. These differentiators are robust to measurement disturbances and may contribute to solving complex control engineering tasks. Critical challenges for the application of the methods are the selection of favourable parameters and their real-time implementation.
This work presents a unified framework for synthesizing and analysing differentiators based on classical orthogonal polynomials. Existing approaches are extended, and their relations to established methods are investigated. Differentia- tors based on Jacobi polynomials, also known as algebraic differentiators, form a particular class of the considered algorithms. Parameter selection guidelines are derived based on filter interpre- tations of the differentiators to achieve desired frequency-domain properties. The discussion of the discrete-time implementation emphasizes the preservation of the latter properties. A new tuning approach based on an optimization problem which requires only the measured signal is proposed. An experimental case study compares the per- formance of the differentiators in the presence
of measurement disturbances. The approximation results, the computational burden, and the storage requirements are discussed in detail. Especially the latter two properties are crucial for real-time applications.
The differentiators are used for model-based fault detection problems in two experimental case studies. First, the collision of a table tennis ball with a magnetically supported plate is discussed. Only the measurement of the plate position and the applied forces are known. The proposed approach significantly reduces the computational burden and memory requirements when compared to previously considered methods. Besides, the new approach decreases the minimum detectable falling height of the ball. Then, a model-based approach for the efficient real-time detection of faults in rolling element bearings is proposed. The approach is validated using experimental data from different test benches.
Finally, a parameter estimation problem is discussed. This work generalises recently proposed algorithms. The derived convergence conditions are less restrictive than the previously published ones. Besides, this approach allows identifying a subset of parameters even if some are not excited. Two experimental case studies validate the theoretical analysis. The results are compared to those achieved using standard gradient estimators and algebraic parameter estimation methods. These examples underline the great potential of these methods.
